Impact of inter-modal four-wave mixing on the performance of mode- and wavelength-division-multiplexing systems

In this paper, we investigate the impact of inter-modal four-wave mixing on mode- and wavelength-division-multiplexing systems. A set of coupled nonlinear Schrödinger equations, including linear mode coupling, is derived allowing to isolate the inter-modal four-wave mixing terms. The efficiency of inter-modal four-wave mixing between degenerate LP modes is found to be significantly higher than the intra-modal four-wave mixing efficiency. However, it is shown that the inter-modal four-wave mixing efficiency between degenerate modes is significantly reduced by the linear mode coupling.

Riccati Representation for Elements in H^(-1) and Its Applications

2002 Mathematics Subject Classification: 35L05, 34L15, 35D05, 35Q53

Resolvent and Scattering Matrix at the Maximum of the Potential

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

Multi-threaded parallel numerical modelling of femtosecond pulse propagation in laser machining

Femtosecond laser microfabrication has emerged over the last decade as a 3D flexible technology in photonics. Numerical simulations provide an important insight into spatial and temporal beam and pulse shaping during the course of extremely intricate nonlinear propagation (see e.g. [1,2]). Electromagnetics of such propagation is typically described in the form of the generalized Non-Linear Schrdinger Equation (NLSE) coupled with Drude model for plasma [3]. In this paper we consider a multi-threaded parallel numerical solution for a specific model which describes femtosecond laser pulse propagation in transparent media [4, 5]. However our approach can be extended to similar models. The numerical code is implemented in NVIDIA Graphics Processing Unit (GPU) which provides an effitient hardware platform for multi-threded computing. We compare the performance of the described below parallel code implementated for GPU using CUDA programming interface [3] with a serial CPU version used in our previous papers [4,5]. © 2011 IEEE.

Gain dependent pulse regimes transitions in a dissipative dispersion-managed fibre laser

For the first time, we demonstrate the possibility to switch between three distinct pulse regimes in a dissipative dispersion-managed (DM) fibre laser by solely controlling the gain saturation energy. Nonlinear Schrödinger equation based simulations show the transitions between hyper-Gaussian similaritons, parabolic similaritons, and dissipative solitons in the same laser cavity. It is also shown that such transitions exist in a wide dispersion range from all-normal to slightly net-normal dispersion. This work demonstrates that besides dispersion and filter managements gain saturation energy can be a new degree of freedom to manage pulse regimes in DM fibre lasers, which offers flexibility in designing ultrafast fibre lasers. Also, the result indicates that in contrast to conservative soliton lasers whose intensity profiles are unique, dissipative DM lasers show diversity in pulse shapes. The findings not only give a better understanding of pulse shaping mechanisms in mode-locked lasers, but also provide insight into dissipative systems.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Weak Langmuir optical turbulence in a fiber cavity

We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave: an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Aside from nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integrodifferential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental setup in which the theoretical predictions can be observed and studied.

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.

Accountability et confiance dans l'institution scolaire

Dans quelle mesure la montée de la reddition de comptes et de l’évaluation en éducation est-elle significative d’un déclin de la confiance de l’Etat, des administrateurs scolaires et des usagers dans la capacité des organisations scolaires à remplir correctement leurs missions ? N’est-elle pas également symptômatique d’une perte de confiance à l’égard des enseignants et de leur professionnalisme? Nous traiterons ces questions en proposant une réflexion à partir des théories de la confiance en sciences sociales. Nous distinguerons en particulier les théories qui s’interrogent sur les conditions de confiance dans les transactions économiques et celles qui raisonnent la confiance « politique » dans les institutions. Nous argumentons que les dispositifs d’accountability tendent surtout à réduire l’incertitude des clients/managers quant aux risques d’opportunisme et d’opacité des opérateurs scolaires. Il s’agit de favoriser la bonne marche « du marché » ou de « l’organisation productive » scolaire, au risque d’une perte d’autonomie professionnelle des enseignants et sans pour autant que l’Ecole ne redevienne une institution politique «digne de confiance ».

Quelques contributions sur les méthodes de Monte Carlo

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Les invariants de la chaleur en dimensions 1 et 2, et application à la hiérarchie de Korteweg-De Vries

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Les interconnexions électriques entre la France et ses voisins européens depuis 1970 : un vecteur méconnu de l'intégration européenne

Les ouvrages de transport d’électricité ont d’abord été pensés un par un, reliant un excédent de production à un besoin de consommation. Ils ont ainsi parfois très naturellement et dès l’origine traversé les frontières des États pour répondre à leur raison d’être. Les secteurs électriques se structurant fortement lorsque le virage électrique fut pris, les interconnexions entre pays furent conçues par les techniciens comme une mesure élémentaire de sûreté et d’équilibre de ce produit atypique qu’est l’électricité. En France plus particulièrement, lorsque la production électronucléaire se développa à partir des années 1970, ces interconnexions devinrent petit à petit sources de revenus pour l’entreprise nationale, et d’équilibre pour la balance commerciale nationale. L’intérêt grandissant porté au secteur électrique par les institutions européennes à la fin des années 1990 vient ébranler les acteurs économiques géographiques verticaux, et rebat les cartes des enjeux à adresser à une maille plus large que l’État nation. Dans ces transformations successives, les interconnexions aux frontières, et particulièrement aux frontières françaises, jouent ainsi un rôle tout à fait spécifique et de plus en plus structurant pour les économies ouvertes des pays européens. Les réseaux de transport électriques continuent ainsi une mutation entamée dans les années 1970 qui les a conduits de la condition de mal nécessaire à celle de vecteurs indispensables de transformation des économies européennes. L’objet de ce mémoire est d’illustrer la très grande capacité d’adaptation de ces organes industriels, économiques, sociétaux et politiques, dont on pourrait faussement penser qu’ils sont immobilisés par leur nature capitalistique, à travers les enjeux portés par les interconnexions aux frontières françaises. Les sources sont à la fois issues de données des opérateurs techniques, de la documentation – encore peu fréquente – sur ces sujets, ainsi que des statistiques officielles du ministère français. Cette capacité d’innovation et de développement de « couches de services » permet aujourd’hui aux grands réseaux de transport de traverser les époques et la variabilité des orientations de leurs environnements, durablement.

Accountability et confiance dans l'institution scolaire

Dans quelle mesure la montée de la reddition de comptes et de l’évaluation en éducation est-elle significative d’un déclin de la confiance de l’Etat, des administrateurs scolaires et des usagers dans la capacité des organisations scolaires à remplir correctement leurs missions ? N’est-elle pas également symptômatique d’une perte de confiance à l’égard des enseignants et de leur professionnalisme? Nous traiterons ces questions en proposant une réflexion à partir des théories de la confiance en sciences sociales. Nous distinguerons en particulier les théories qui s’interrogent sur les conditions de confiance dans les transactions économiques et celles qui raisonnent la confiance « politique » dans les institutions. Nous argumentons que les dispositifs d’accountability tendent surtout à réduire l’incertitude des clients/managers quant aux risques d’opportunisme et d’opacité des opérateurs scolaires. Il s’agit de favoriser la bonne marche « du marché » ou de « l’organisation productive » scolaire, au risque d’une perte d’autonomie professionnelle des enseignants et sans pour autant que l’Ecole ne redevienne une institution politique «digne de confiance ».

Quelques contributions sur les méthodes de Monte Carlo

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.